/// <summary>
/// 检查所给点集是否为顺时针排序(向量叉乘的法线朝向)
/// </summary>
/// <returns></returns>
public static bool CheckVector(List <Vector3> points)
{
// 创建一个除去自身的 多边形，判断是否为内点（凹点）
List <Vector3> polygon = new List <Vector3>(points);
polygon.RemoveAt(0);
Vector3 vector3_1 = points[0] - points[1];
Vector3 vector3_2 = points[points.Count - 1] - points[0];
Vector3 nom = Vector3.Cross(vector3_1, vector3_2); // 算出法线方向。Unity为左手坐标系, 使用左手定则
//是否是凹点
if (Math2d.IsPointInsidePolygon(points[0], polygon))
{
// 法线方向朝下。即逆时针排序，需要反转
if (nom.y < 0)
{
return(false);
}
}
else // 凸点
{
// 法线方向朝上。即逆时针排序，需要反转
if (nom.y > 0)
{
return(false);
}
}
return(true);
}
/// <summary>
/// 返回三角形的内部(整数)顶点
/// </summary>
/// <param name="trianglePoints">三角形的三个顶点</param>
/// <returns></returns>
public static List <Vector3> GetPointsInTriangle(List <Vector3> trianglePoints)
{
// 取出所围的四边形
float xMin = Mathf.Min(Mathf.Min(trianglePoints[0].x, trianglePoints[1].x), trianglePoints[2].x);
float zMax = Mathf.Max(Mathf.Max(trianglePoints[0].z, trianglePoints[1].z), trianglePoints[2].z);
float zMin = Mathf.Min(Mathf.Min(trianglePoints[0].z, trianglePoints[1].z), trianglePoints[2].z);
List <Vector3> InsidePoints = new List <Vector3>(); // 内部点集
Vector3 pointTmp = Vector3.zero; // 临时点
List <Vector3> crossPoints = new List <Vector3>(); // 交点点集（2个点）
// 遍历四边形的内部所有点
for (int z = (int)zMin, iLength = (int)zMax + 1; z < iLength; z++)
{
pointTmp.Set(xMin, 0, z); // 设置临时点(固定x，将z递增)
Math2d.IsPointInsidePolygon(pointTmp, trianglePoints.ToArray(), out crossPoints); // 获取z轴平行线与三角形的交点
// 循环添加两个交点之间的网格点
for (int x = (int)crossPoints[0].x, length = (int)crossPoints[crossPoints.Count - 1].x + 1; x < length; x++)
{
InsidePoints.Add(new Vector3(x, 0, z));
}
}
return(InsidePoints);
}
/// <summary>
/// 获取两点组成的矩形边框
/// </summary>
/// <param name="start">起始点</param>
/// <param name="end">终止点</param>
/// <param name="width">宽度</param>
/// <returns></returns>
public static Vector2[] GetRect(Vector2 start, Vector2 end, float width)
{
Vector2[] rect = new Vector2[4];
Vector2 dir = Math2d.GetHorizontalDir(end - start);
rect[0] = start + dir * width;
rect[1] = start - dir * width;
rect[2] = end + dir * width;
rect[3] = end - dir * width;
return(rect);
}
/// <summary>
/// 通过给定网格间隔，获取三角形内部的网格点
/// </summary>
/// <param name="trianglePoints">三角形顶点</param>
/// <param name="pieceX">X的间隔</param>
/// <param name="pieceZ">Z的间隔</param>
/// <returns></returns>
public static List <Vector3> GetPointsInTriangle(Vector3[] trianglePoints, float pieceX, float pieceZ)
{
float halfX = 0.5f * pieceX;
float halfZ = 0.5f * pieceZ;
// 归置三角形顶点
for (int i = 0; i < trianglePoints.Length; i++)
{
trianglePoints[i].x = trianglePoints[i].x - trianglePoints[i].x % pieceX + halfX;
trianglePoints[i].z = trianglePoints[i].z - trianglePoints[i].z % pieceZ + halfZ;
}
// 取出所围的四边形
float xMin = Mathf.Min(trianglePoints[0].x, trianglePoints[1].x, trianglePoints[2].x);
xMin = xMin - xMin % pieceX - halfX; // 取到所在的网格中心点
float zMax = Mathf.Max(trianglePoints[0].z, trianglePoints[1].z, trianglePoints[2].z);
zMax = zMax + zMax % pieceZ + halfZ;
float zMin = Mathf.Min(trianglePoints[0].z, trianglePoints[1].z, trianglePoints[2].z);
zMin = zMin - zMin % pieceZ - halfZ;
List <Vector3> InsidePoints = new List <Vector3>(); // 内部点集
Vector3 pointTmp = Vector3.zero; // 临时点
List <Vector3> crossPoints = new List <Vector3>(); // 交点点集（2个点）
// 遍历四边形的内部所有点
for (float z = zMin; z <= zMax; z += pieceZ)
{
pointTmp.Set(xMin, 0, z); // 设置临时点(固定x，将z递增)
Math2d.IsPointInsidePolygon(pointTmp, trianglePoints, out crossPoints); // 获取z轴平行线与三角形的交点
if (crossPoints.Count == 2)
{
// 循环添加两个交点之间的网格中心点
for (float x = Mathf.Min(crossPoints[0].x, crossPoints[1].x); x <= Mathf.Max(crossPoints[0].x, crossPoints[1].x); x += pieceX)
{
InsidePoints.Add(new Vector3(x, 0, z));
}
}
crossPoints.Clear();
}
return(InsidePoints);
}
/// <summary>
/// 将一个多边形转化为多个三角形
/// </summary>
/// <param name="points"></param>
/// <returns></returns>
public static List <Vector2[]> PolygonToTriangles(List <Vector2> points)
{
if (points.Count < 3)
{
return(null);
}
List <Vector2[]> triangles = new List <Vector2[]>();
int index = points.Count - 1;
int next;
int prev;
while (points.Count > 3)
{
List <Vector2> polygon = new List <Vector2>(points);
polygon.RemoveAt(index);
//是否是凹点
if (!Math2d.IsPointInsidePolygon(points[index], polygon.ToArray(), false))
{
// 是否是可划分顶点:新的多边形没有顶点在分割的三角形内
if (IsFragementIndex(points, index, false))
{
//可划分，剖分三角形
next = (index == points.Count - 1) ? 0 : index + 1;
prev = (index == 0) ? points.Count - 1 : index - 1;
triangles.Add(new Vector2[]
{
points[index],
points[prev],
points[next]
});
points.RemoveAt(index);
index = (index + points.Count - 1) % points.Count; // 防止出现index超出值域
continue;
}
}
index = (index + 1) % points.Count;
}
triangles.Add(new Vector2[] { points[1], points[0], points[2] });
return(triangles);
}
/// <summary>
/// 获取扇形区域的点集合（包括圆心点）没有地平线以下的区域
/// </summary>
/// <param name="origin">圆心点</param>
/// <param name="tarPoint"></param>
/// <param name="alpha">x,z轴张角</param>
/// <param name="theta">x,y轴张角</param>
/// <returns></returns>
public static Vector3[] GetSectorPoints_2(Vector3 origin, Vector3 tarPoint, float alpha, float theta)
{
List <Vector3> points = new List <Vector3>();
int halfAlpha = (int)(alpha / 2);
Vector3 startVector_1 = tarPoint - origin; // 获取底面中间向量
float tempHeight = Mathf.Tan(theta * Mathf.Deg2Rad) * startVector_1.magnitude; // 扇形区域最边缘高度
// 获取扇形下表面和下表面的半径
float radiusDown = (tarPoint - origin).magnitude;
float radiusUp = radiusDown / Mathf.Cos(theta * Mathf.Deg2Rad); // 获得扇形顶面半径
// 获取扇形弧边所有点的方向向量
List <Vector3> dirsDown = new List <Vector3>();
List <Vector3> dirsUp = new List <Vector3>();
for (int i = -halfAlpha, j = 0; i <= halfAlpha; i += 3, j++)
{
// 获取下弧边的方向向量
Vector2 temp = Math2d.GetTargetVector(new Vector2(startVector_1.x, startVector_1.z), i);
dirsDown.Add(new Vector3(temp.x, 0, temp.y));
// 获取上弧边的方向向量
Vector3 targetDir = temp.magnitude / Mathf.Cos(i * Mathf.Deg2Rad) * dirsDown[j].normalized + Vector3.up * tempHeight;
dirsUp.Add(targetDir);
}
// 获取扇形所有点
points.Add(origin);
for (int i = 0; i < dirsDown.Count; i++)
{
points.Add(dirsDown[i].normalized * radiusDown + origin);
}
points.Add(origin);
for (int i = 0; i < dirsUp.Count; i++)
{
points.Add(dirsUp[i].normalized * radiusUp + origin);
}
return(points.ToArray());
}
/// <summary>
/// 以index点和前后两个点构造一个三角形,判断点集内的其余点是否全部在这个三角形外部(忽略y轴)
/// </summary>
public static bool IsFragementIndex(List <Vector3> verts, int index, bool containEdge = true)
{
int len = verts.Count;
List <Vector3> triangleVert = new List <Vector3>();
int next = (index == len - 1) ? 0 : index + 1;
int prev = (index == 0) ? len - 1 : index - 1;
triangleVert.Add(verts[prev]);
triangleVert.Add(verts[index]);
triangleVert.Add(verts[next]);
for (int i = 0; i < len; i++)
{
if (i != index && i != prev && i != next)
{
if (Math2d.IsPointInsidePolygon(verts[i], triangleVert.ToArray(), containEdge))
{
return(false);
}
}
}
return(true);
}